A box contains 3 red and 2 black balls and another box contains 2 red and 4 black balls. One box chosen at random. From the selected box one ball is drawn. The probability of getting a red ball is

A can solve 90% problems and B can solve 70% problems of the book. A problem is selected at random from the book. The probability that the problem is solved, is equal to

Which is the most suitable definition for random variable among the options given below:

If A and B are two events such that $P(A) = \frac{1}{2}$, $P(B) = \frac{1}{3}$, $P(B|A) = \frac{1}{4}$, then $P(A|B)$ is:

A letter is known to have come either from KOLKATA or TATANAGAR. On the envelope just two consecutive letters TA are visible. The probability that letter has come from TATANAGAR is

Suppose X has Poisson distribution such that $3 P(X=1) = 2 P(X=2)$ then $P(X>0)$ is:

Mean and variance of a binomial distribution are 6 and 2 respectively. The probability of 2 successes will be